On inverse sum indeg energy of graphs

Fareeha Jamal, Muhammad Imran, Bilal Ahmad Rather

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


For a simple graph with vertex set {v1, v2, ⋯, vn} and degree sequence dvi i = 1, 2, ⋯, n the inverse sum indeg matrix (ISI matrix) AISI(G) = (aij) of G is a square matrix of order n, where aij = dvidvj/dvi + dvj, if vi is adjacent to vj and 0, otherwise. The multiset of eigenvalues τ1 ≥ τ2 ≥ ⋯ ≥ τn of AISI(G) is known as the ISI spectrum of G. The ISI energy of G is the Σni=1 |τ| of the absolute ISI eigenvalues of G. In this article, we give some properties of the ISI eigenvalues of graphs. Also, we obtain the bounds of the ISI eigenvalues and characterize the extremal graphs. Furthermore, we construct pairs of ISI equienergetic graphs for each n≥ 9.

Original languageEnglish
JournalSpecial Matrices
Issue number1
Publication statusPublished - Jan 1 2023


  • adjacency matrix
  • energy
  • inverse sum indeg matrix
  • topological indices

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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